I've got a new modem/gateway/router/switch/AP and configured it. So the temporary modem from my girlfriend can go back to her place.
The device possibilities are quite extended, although I think the configuration (at least the web configuration) doesn't offer all possibilities I'd like, but nothing I can't live with.
And this time I did check if my server was reachable from the internet... 
Of course, it would have been a good idea to test whether my server was reachable from the internet (which it wasn't)... I forgot to configure the NAT section of the modem, which means no NAT at all...
Stupid me!
But now, finally, my server is reachable again.
I've borrowed a modem from my girlfriend, as she doesn't need it now herself, because her ADSL line still isn't working since she moved. This will of course only be temporary, but she'll probably lend it even when her ADSL line starts working, but I hope my internet provider will be willing to supply a new modem to me and that it will happen soon.
Then my internet connection will of course go offline for a while when connecting and configuring that new modem, but hopefully it won't take much time (as it will be supplied by my internet provider and will be pre-configured by them to working values).
But finally, I've got a life again, after being (almost entirely) disconnected for a few days...